Abstract
Computing energy transfer between objects is the most expensive operation in radiosity systems. This energy transfer operation, known as the irradiance operator, is an integral that, in general, must be calculated numerically. We perform a study of numerical integration techniques to increase the speed of this computation without severely compromising fidelity. A theoretical discussion of numerical integration is presented followed by details of the studied methods. The results of our study give us insight into greatly reducing the cost of the irradiance operator while maintaining accuracy. An adaptive method for choosing Gauss quadrature rules is presented, and our performance analysis of the new adaptive algorithm shows that it can be up to 10 times faster than previous methods.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cohen, M. F., and Greenberg, D. P. The hemicube: A radiosity solution for complex environments. Computer Graphics 19, 3 (July 1985), 31–40.
Cohen, M. F., and Wallace, J. R. Radiosity and Realistic Image Synthesis. Academic Press Professional, Boston, 1993.
Gershbein, R., Schröder, P., and Hanrahan, P. Textures and radiosity: Controlling emission and reflection with texture maps. In Computer Graphics 1994 ( August 1994 ), Siggraph, pp. 51–58.
Goral, C. M., Torrance, K. E., Greenberg, D. P., and Battaile, B. Modelling the interaction of light between diffuse surfaces. Computer Graphics 18, 3 (July 1984), 212–222.
Gortler, S., Schröder, P., Cohen, M., and Hanrahan, P. Wavelet radiosity. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 221–230.
Hanrahan, P., Salzman, D., and Aupperle, L. A rapid hierarchical radiosity algorithm. Computer Graphics 25, 4 (July 1991), 197–206.
Heckbert, P. S. Radiosity in flatland. Computer Graphics Forum 2,3 (1992), 181–192.
Kajiya, J. T. The rendering equation. Computer Graphics 20, 4 (1986), 143–150.
Kalos, M. H., and Whitlock, P. A. Monte Carlo Methods Volume I: Basics. Whiley-Interscience, New York, 1986.
Lischinski, D., Tampieri, F., and Greenberg, D. P. Combining hierarchical radiosity and discontinuity meshing. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 199–208.
Schröder, P. Numerical integration for radiosity in the presence of singularities. In Fourth Eurographics Workshop on Rendering (1993).
Schröder, P., Gortler, S. J., Cohen, M. F., and Hanrahan, P. Wavelet projections for Radiosity. IN Fourth Eurographics Workshop On Rendering (June 1993), Eurographics, PP. 105–114.
Schröder, P., AND Hanrahan, P. On the form factor between two polygons. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 163 - 164.
Shirley, P. Discrepancy as a quality measure for sampling distributions. In Eurographics ’91 (September 1991), pp. 183–193.
Smits, B., Arvo, J., and Greenburg, D. A clustering algorithm for radiosity in complex environments. In Computer Graphics 1994 ( August 1994 ), Siggraph, pp. 435–442.
Stoer, J., and Bulirsch, R. Introduction to Numerical Analysis. Springer Verlag, New York, 1980.
Stroud, A. H. Approximate Calculation of Multiple Integrals. Prentice-Hall, New Jersey, 1971.
Teller, S., and Hanrahan, P. Global visibility algorithms for illumination computations. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 239–246.
Troutman, R., andMax, N. Radiosity algorithms using higher-order finite elements. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 209–212.
Zatz, H. R. Galerkin radiosity: A higher-order solution method for global illumination. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 213–220.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag/Wien
About this paper
Cite this paper
Gershbein, R. (1995). Integration Methods for Galerkin Radiosity Couplings. In: Hanrahan, P.M., Purgathofer, W. (eds) Rendering Techniques ’95. EGSR 1995. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9430-0_25
Download citation
DOI: https://doi.org/10.1007/978-3-7091-9430-0_25
Published:
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82733-8
Online ISBN: 978-3-7091-9430-0
eBook Packages: Springer Book Archive